In 1978, French artist Orlan was preparing to speak at a symposium on video and performance art when she had to be taken to hospital for emergency surgery. "I almost died because I had an ectopic pregnancy," she recalls as we sit in her studio in Paris. "They had to operate to save my life and remove what they told me was a non-viable foetus."

Orlan took a video crew along to film the operation and insisted she remain conscious throughout. "I wasn't in pain and what was happening to my body was of profound interest to me," she explains. "Pain is an anachronism. I have great confidence in morphine."

What she saw and filmed that day, 31 years ago, inspired her career. Orlan saw the surgeon as a priest-like figure, his assistants gathered around him like fellow celebrants at a Catholic mass. The light from above recalled the heavenly beams that shine down in Bernini's baroque sculpture of Saint Teresa, writhing in religious ecstasy. "For many years, I had appropriated baroque imagery in my work, especially in relation to Catholic art. So when I lay on the operating table, the parallels between the operating theatre and the Catholic mass were not wasted on me."

It was at 15 that she stopped being Mireille Suzanne Francette Porte from Saint-Étienne and was reborn as Orlan, a name freighted with symbolic import. Her subsequent career has been a series of rebirths and triumphs of will over technology. In 1964, she presented a nude photograph of herself, shot from above, giving birth to an androgynous mannequin, entitled Orlan S'Accouche d'Elle M'Aime (a punning French title perhaps best translated as Orlan Gives Birth to Her Beloved Self). She later reinvented herself as a saint, calling her series of performance-surgeries The Reincarnation of Saint-Orlan.

More importantly, Orlan saw that she had a double role in what was going on: she was both observer and observed. For a feminist artist long troubled by women's historic role in art (largely undressed and on the receiving end of the male gaze), this was a revelatory moment. She decided to go under the knife again and again – not because her life was at risk, but because she believed surgically changing her body could be a powerful work of art.

From 1990 to 1995, she underwent nine plastic surgery operations, intending to rewrite western art on her own body. One operation altered her mouth to imitate that of François Boucher's Europa, another changed her forehead to mimic the protruding brow of Leonardo's Mona Lisa, while yet another altered her chin to look like that of Botticelli's Venus.

Was she trying make herself more beautiful? "No, my goal was to be different, strong; to sculpt my own body to reinvent the self. It's all about being different and creating a clash with society because of that. I tried to use surgery not to better myself or become a younger version of myself, but to work on the concept of image and surgery the other way around. I was the first artist to do it," she says, proudly.

When she had plastic surgery on her brow in New York in 1993, Olan emerged with two little implants – usually used to enhance cheekbones – on either side of her forehead. Hostile critics called them "demon horns", but they are more like nascent antlers. Today as we chat, I notice she has decorated them with glitter eyeliner to accentuate their presence. They sparkle under the camera's lights.

But is it her aim to change the idea of beauty? "I am not sure I can change such a thing, but I can produce images that are different from those we find in comics, video games, magazines and TV shows. There are other ways to think about one's body and one's beauty. If you were to describe me without anyone being able to see me, they would think I am a monster, that I am not fuckable. But if they see me, that could perhaps change."

Orlan's operating table became her baroque theatre. Designers, such as Paco Rabanne and Issey Miyake, created costumes for Orlan to wear during the surgeries. Poetry was read and music played while she lay fully conscious. Each surgery was captured on video, broadcast in galleries and sometimes fed to audiences around the globe via live satellite link-ups.

Some critics have described Orlan as mad, some have written up her interest in cosmetic surgery as anti-feminist. But it's no madder than what Joseph Beuys did in 1965, when he painted himself in gold, strapped a ski to one foot, and sat in an exhibition space explaining pictures to a dead rabbit he held in his arms. He called the piece How to Explain Pictures to a Dead Hare.

And truthfully, Orlan is pretty sane. She greets me courteously at her studio and responds thoughtfully to every question I ask her. Her work isn't all as controversial as the performance-surgeries; much of it is straightforward feminist critiques of male, western art. On the wall as we talk is her photo of a reclining man's genitals, penis erect. It's a riff on Gustave Courbet's L'Origine Du Monde (The Origin of the World), depicting a woman's genitals. Orlan calls her version The Origin of War.

But there's no denying that most of her art is troubling. In this studio where Orlan lives with her husband, art historian and writer Raphael Cuir, she shows me what she calls a "reliquary of flesh", material left over from her surgeries. She picks it up and offers it to me: "This is my body, my software," she says with a giggle. Once, on a TV show, she offered some of it to Madonna. "[Madonna] said it was like caviar. She probably eats a lot of it, and knows what she's talking about."

Orlan looks the part of a radical artist. Her Cruella de Vil-style hairdo is perfectly coiffed and she wears noisily coloured designer spectacles with shouty tights (one leg yellow, the other pink). After the interview, we head off to the Pompidou Centre to see a new exhibition featuring her work. Gallic jaws drop as she sweeps majestically along, muttering crossly: "Merde! Where did I leave my car?" She ignores the stares of people in cafes, and I trail behind her, grey-clad and surgically unenhanced, as Orlan's uninteresting shadow.

To her, what she does is "carnal art", which can be distinguished from body art. The latter she takes to involve personal risk and be mostly the preserve of men. An example would be Trans-fixed by Chris Burden, who in 1974 had himself nailed through the hands to a VW Beetle, in a piece that conflated crucifixion imagery with consumerism. "I like body art, but it's not my thing," says Orlan. "I am all for pleasure and sensuality, not for endurance and suffering."

So, what is carnal art? According to Orlan's Carnal Art Manifesto, it's "not against cosmetic surgery, but rather against the conventions carried by it and their subsequent inscription". As I read it, carnal art is also anti-Christian. Orlan isn't fussed. "Religion is always against women, and Christian art wants us to not touch bodies, to choose between good and evil. But all my work is about good and evil. So for me God isn't a solution for my life, or for my work."

She says her work is a "struggle against the innate, the inexorable, the programmed, nature, DNA – and God." She also believes it is important to underline her work as a feminist artist. "All my life I came second, as men were always coming first. Not to talk about feminism would mean that I didn't respect myself."

As an artist, she is undaunted by controversy. In 1978, she displayed her menstruating genitals under a magnifying glass in a performance piece called Documentary Study: The Head of Medusa, subverting a motto she had taken from a Sigmund Freud text: "At the sight of the vulva, even the devil runs away."

I wonder if her years of sensationalism and surgery are over. "Surgery is something I haven't done for a long time," she says, as we stroll among her artworks in the Pompidou Centre. "I have done sculptures, photographic works, installations, performances, biotechnology, but I always try to change materials and style to find the best solution."

As we finish the interview, Orlan kisses me and I resist the urge to kiss her forehead lumps rather than her cheeks. I finally ask if she still wants to scandalise through her art? "I expect to do just that in September when I present an installation in the Casino in Luxembourg," she says. The piece will use a bioreactor to cultivate her cells among those of other humans and animals. As she says: "Everyone is scared of genetic DIY. It's crucial for artists to work with such technologies. It is important that we work between science and art." Especially if you're a woman? "Oh yes, everything takes a different flavour when a woman does it."